Noise in the power line may be coupled between devices and boards through power supply connections. Power supply decoupling(bypass) capacitors help to reduce this effect. Since a capacitor is a frequency-dependant impedance, its value should be adjusted according to the operating or noise frequency.

Capacitors contain series inductance(ESL) which causes resonance at the Self Resonant Frequency(SRF). At this frequency the impedance of the capacitor is lowest. Above the SRF, the impedance of the capacitor starts to increase. The larger the capacitor value, the lower the SRF. So the capacitor(s) should be chosen with a SRF that is greater than the noise that you are attempting to remove.

It is common to use two or more capacitors in parallel (refer to example ADL5375 IQ Modulator Schematic) on the power supply line, one to work on lower frequency noise and the other to work on higher frequency noise. If one specific value works better than others, it indicates there could be significant power supply noise at or near the capacitor's SRF. If the same capacitor value is available in a variety of sizes, the smaller size is better becasue it has smaller ESL. Ceramic capacitors are widely used for this purpose because of good performance over a wide range of values and low cost. The decoupling (bypass) capacitor should be placed as close as possible to the power supply pin to minimize additional series inductance, which will lowers the effective SRF of the capacitor.

You can calculate the correct capacitor values by first checking which noise frequencies are present on the board, and which of these need to be decoupled. For this purpose, vendors such as Murata provide software to calculate the impedance vs. frequency response for different capacitor values and package sizes. Below is one example derived from that software.

This also applies to the selection of AC coupling capacitors in the signal path. In this case, the capacitor should be chosen so that it presents as little impedance as possible at the signal frequency, resulting in minimum power loss..